The Standard Normal Distribution Quiz

PDF page 388: The standardized normal distribution is a type of normal distribution, with a mean of 0 and standard deviation of 1. It represents a distribution of standardized scores, called z-scores, as opposed to raw scores (the actual data values). A z-score indicates the number of standard deviation a score falls above or below the mean. Z-scores allow for comparison of scores, occurring in different data sets, with different means and standard deviations. It would not make sense to compare apples and oranges. Likewise, it does not make sense to compare scores from two different samples that have different means and standard deviations. Z-scores can be looked up in a Z-Table of Standard Normal Distribution, in order to find the area under the standard normal curve, between a score and the mean, between two scores, or above or below a score. The standard normal distribution allows us to interpret standardized scores and provides us with one table that we may use, in order to compute areas under the normal curve, for an infinite number of data sets, no matter what the mean or standard deviation. x − μ . The score itself can be found by using algebra and solving for x. Multiplying both A z-score is calculated as z = σ

PDF page 388: The standardized normal distribution is a type of normal distribution, with a mean of 0 and standard deviation of 1. It represents a distribution of standardized scores, called z-scores, as opposed to raw scores (the actual data values). A z-score indicates the number of standard deviation a score falls above or below the mean. Z-scores allow for comparison of scores, occurring in different data sets, with different means and standard deviations. It would not make sense to compare apples and oranges. Likewise, it does not make sense to compare scores from two different samples that have different means and standard deviations. Z-scores can be looked up in a Z-Table of Standard Normal Distribution, in order to find the area under the standard normal curve, between a score and the mean, between two scores, or above or below a score. The standard normal distribution allows us to interpret standardized scores and provides us with one table that we may use, in order to compute areas under the normal curve, for an infinite number of data sets, no matter what the mean or standard deviation. x − μ . The score itself can be found by using algebra and solving for x. Multiplying both A z-score is calculated as z = σ

PDF page 388: The standardized normal distribution is a type of normal distribution, with a mean of 0 and standard deviation of 1. It represents a distribution of standardized scores, called z-scores, as opposed to raw scores (the actual data values). A z-score indicates the number of standard deviation a score falls above or below the mean. Z-scores allow for comparison of scores, occurring in different data sets, with different means and standard deviations. It would not make sense to compare apples and oranges. Likewise, it does not make sense to compare scores from two different samples that have different means and standard deviations. Z-scores can be looked up in a Z-Table of Standard Normal Distribution, in order to find the area under the standard normal curve, between a score and the mean, between two scores, or above or below a score. The standard normal distribution allows us to interpret standardized scores and provides us with one table that we may use, in order to compute areas under the normal curve, for an infinite number of data sets, no matter what the mean or standard deviation. x − μ . The score itself can be found by using algebra and solving for x. Multiplying both A z-score is calculated as z = σ

PDF page 389: As described previously, if X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is x – μ z = . σ The z-score tells you how many standard deviations the value x is above, to the right of, or below, to the left of, the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero. When determining the z-score for an x-value, for a normal distribution, with a given mean and standard deviation, the notation above for a normal distribution, will be given.

PDF page 389: Suppose we have a data set with a mean of 5 and standard deviation of 2. We want to determine the number of standard deviations the score of 11 falls above the mean. We can find this answer (or z-score) by writing 11 − 5 z = = 3 2 or 5 + (z)(2) = 11, we can solve for z. 2z = 6 z = 3

PDF page 389: We have determined that the score of 11 falls 3 standard deviations above the mean of 5. With a standard normal distribution, we indicate the distribution by writing Z ~ N(0, 1) which shows the normal distribution has a mean of 0 and standard deviation of 1. This notation simply indicates that a standard normal distribution is being used.

PDF page 389: As described previously, if X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is x – μ z = . σ The z-score tells you how many standard deviations the value x is above, to the right of, or below, to the left of, the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero. When determining the z-score for an x-value, for a normal distribution, with a given mean and standard deviation, the notation above for a normal distribution, will be given.

PDF page 389: As described previously, if X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is x – μ z = . σ The z-score tells you how many standard deviations the value x is above, to the right of, or below, to the left of, the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero. When determining the z-score for an x-value, for a normal distribution, with a given mean and standard deviation, the notation above for a normal distribution, will be given.

PDF page 389: Suppose X ~ N(5, 6). This equation says that X is a normally distributed random variable with mean μ = 5 and

PDF page 389: x – μ 17 – 5 z = = = 2. σ 6

PDF page 389: This means that x = 17 is two standard deviations (2σ) above, or to the right, of the mean μ = 5.

PDF page 389: Notice that 5 + (2)(6) = 17. The pattern is μ + zσ = x.

PDF page 388: sides of the equation by σ gives: (z)(σ) = x − μ . Adding μ to both sides of the equation gives μ + (z)(σ) = x .

PDF page 389: indicates how far the score is from the mean, in either direction.

PDF page 390: a. This z-score tells you that x = 10 is 2.5 standard deviations to the right of the mean five.